Question

If a1 = 1 and an = (an-1)2 – 4 then find the value of a4.

Answer 1

Step 1: Write out the formula for nth term

$a_n=(a_{n-1})^2-4$

Step 2: Write out the 4th term

$a_4=a^2_3-4$

Step 3: Write out the 3rd term

$a_3=a^2_2-4$

Step 4: Write out the 2nd term

$a_2=a^2_1-4$

Step 5: Substitute the value of a1 into the formula for the 2nd term

$a_2=(1)^2-4=1-4=-3$

Step 6: Substitute the value of a2 into the formula for the 3rd term

$a_3=(-3)^2-4=9-4=5$

Step 7: Substitute the value of a3 into the formula for the 4th term

$a_4=(5)^2-4=25-4=21$

Hence, the value of a4 is 21